Meteors burn up in Earth's atmosphere. They are made of microscopic rocks - such as granite- and ice. They are also a streak of light in the sky produced by the burning of a meteoroid. You probably know them as "shooting stars".
A comet is a dirty snow ball with vents that release gas into space. It's made of materials left over from the formation of the universe (water, carbon dioxide and organic compounds).It's a mixture of ice and dust. The ice in it sublimates off the nucleus when the comet gets near the sun. It's dust tail is the part of the comet easiest to see.
Asteroids are generally larger chunks of rock that come from the asteroid belt between Mars and Jupiter. They are metallic, rocky bodies without atmosphere that orbit the Sun, but are too small to be classified as planets.